There’s a small section of vertical pipe that tees off from behind the tub faucet. There’s a valve keeping it shut. When you switch to shower mode, you open the valve. The pressurized water coming from the water heater will force its way up the vertical pipe, but the pipe is full of water from the last time you had a shower. So first the old water that’s sitting in the pipe has to get pushed out of the way, and that water is cold (or at least, room temperature) because it’s been sitting in the pipe.
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